For a matrix \({\bf A}\)  on a graph \({\mathcal {G}}=(V, E)\) , define its Schur norm by
\(\Vert {\bf A}\Vert _{\mathcal {S}}=\max _{i\in V} P_{\bf A}(i,i)\) , where \(P_{\bf A}(i,i), i\in V\) , are given by (REF )
[1]}, [2]}.
For the case that the constant \(c\) 
in
(REF ) and (REF ) is so chosen that
\(c\ge \Vert {\bf A}\Vert _{\mathcal {S}}\) ,
the preconditioning matrices \({\bf Q}_c\)  and
\({\bf Q}_c^{\rm sym}\)  become a multiple of the identity matrix \({\bf I}\)  and
the corresponding PGDA and SPGDA are
the conventional gradient descent algorithm and its symmetric version
respectively [3]}, [4]}, [5]}, [2]}, [7]}.
We denote the above
algorithms with \(c=\Vert {\bf A}\Vert _{\mathcal {S}}\) 
by GDASchur and SGDASchur respectively, see Figure REF  for their performance.
Since 1 is the maximal eigenvalue of matrices \({\bf H}_{0, m}^{\rm spln}, m\ge 1\) ,
we can use
the conventional power iteration method with entries of the initial \({\bf x}_0\)  randomly selected in \([0, 1]\) , POWER for abbreviation,
to find principal eigenvectors [8]}.
Presented in
Figure REF  is its performance.
From Figure REF , we observe that
the centralized algorithm POWER has fastest convergence
to find eigenvectors of matrices \({\bf H}_{0, m}^{\rm spln}, 2\le m\le 4\) ,
as followed are the distributed algorithm SPGDA, the centralized algorithm SPGDASchur and the distributed algorithm SPGDA1h,
the next are the distributed algorithm PGDA and the centralized algorithm GDASchur, and the distributed algorithm PGDA1h has slowest convergence.
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